Well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices

Details Well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices Well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices

2003-07-31

arxiv.org/abs/math/0307400v1

Mathematics

Analysis of PDEs

Scientific paper

We prove that, the initial value problem associated to u_{t} + i\alphau_{xx}
+ \beta u_{xxx} + i\gamma |u|^{2}u = 0, x,t \in R, is locally well-posed in
Sobolev spaces H^{s} for s>-1/4.

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